Question

A particle, moving with uniform speed $v$, changes its direction by angle $\theta$ in time $t$. Magnitude of its average acceleration during this time is

• A. $\text{Zero}$
• B. $\frac{2v}{t}\text{sin}\frac{\theta }{2}$
• C. $\frac{v\sqrt{2}}{t}$
• D. $\text{None of these}$

Answer 1

The correct option is B $\frac{2v}{t}\text{sin}\frac{\theta }{2}$

$|a_{av}|=\left|\frac{\Delta v}{\Delta t}\right|=\frac{|v_f-v_i|}{t}$
$=\frac{\sqrt{v^2+v^2-2v\cdot v\cos \theta }}{t}$
$=\frac{2v\sin \frac{\theta }{2}}{t}$